Question

An isotope of gallium, ⁶⁷Ga, has an atomic number of 31 and a half-life of 78 hours. Consider a small mass of 3.9 grams for ⁶⁷Ga which is initially pure.

1) Initially, what is the half-life of the gallium?

T_1/2o =

2) Initially, what is the initial decay constant of the Ga atom in the sample?

λ_o =

3) Initially, what is the decay rate of the gallium?

R_o =

4) What is the half-life of the gallium after 24 hours?

T_1/21 =

5) Initially, what is the initial decay constant of the Ga atoms after 24 hours?

λ₁ =

6) What is the decay rate of the gallium after 24 hours?

R₁ =

Answer 1

1) Initial t1/2=78hrs

2)initial decay constant=0.693/t1/2

=0.693/78

=0.0089/hr or

​32.04/sec

3)decay rate = decay constant*number of particles

=(0.0089*3.9*6.023*10²³)/67

=3.12*10²³particles per hr

Or 3.024*10¹⁶ Cu

4)Half life remains same after 24 hrs

5)Decay constant remains same after 24 hrs

6)decay rate= decay constant *no. of particles

The math is attatched as an image